Covariant Newtonian and Relativistic dynamics of (magneto)-elastic solid model for neutron star crust

TL;DR

This paper develops a covariant model for the dynamics of magneto-elastic solids in neutron star crusts, deriving explicit formulas for wave speeds in both relativistic and Newtonian regimes.

Contribution

It introduces a fully covariant formulation of magneto-elastic dynamics applicable to neutron star crusts, bridging relativistic and Newtonian descriptions.

Findings

Derived explicit formulas for magneto-elastic wave speeds.

Unified covariant framework for relativistic and Newtonian models.

Enhanced understanding of neutron star crust dynamics.

Abstract

This work develops the dynamics of perfectly elastic solid model for application to the outer crust of a magnetised neutron star. Particular attention is given to the Noether identities responsible for energy-momentum conservation, using a formulation that is fully covariant, not only (as is usual) in a fully relativistic treatment but also (sacrificing accuracy and elegance for economy of degrees of gravitational freedom) in the technically more complicated case of the Newtonian limit. The results are used to obtain explicit (relativistic and Newtonian) formulae for the propagation speeds of generalised (Alfven type) magneto-elastic perturbation modes.